Scattering by microspheres or microcylinders is already a perfectly solved problem, the history of which can be traced as far back as Mie, “Contributions to the optics of turbid media, particularly of colloidal metal solutions,” Ann. Phys., vol. 25, pp. 377-445 (1908), which provides the analytic solution of scattering by spherical gold particles, and which is incorporated herein by reference.
In 2000, this topic once again generated widespread attention when Lu et al., “Laser writing of a subwavelength structure on silicon (100) surfaces with particle-enhanced optical irradiation,” JETP Lett., vol. 72, pp. 457-59, (2000), incorporated herein by reference, reported that an enhanced laser irradiation generated on the shadow side surface of an illuminated dielectric microsphere can write a subwavelength structure on a silicon surface. The enhanced irradiation was named a “photonic nanojet” (PNJ) by Chen et al., “Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express, vol. 12, pp. 1214-20 (2004) (hereinafter, “Chen 2004”), incorporated herein by reference.
By using rigorous Mie theory combined with a Debye series expansion, Itagi et al., “Optics of photonic nanojets,” J. Opt. Soc. Am. A, vol. 22, pp. 2847-58 (2005), incorporated herein by reference, demonstrated that the focusing behavior of a microsphere or microcylinder is significantly different from that of the conventional solid immersion lens. Particular features of focusing by microspheres or microcylinders enable potentially important applications in the areas of nanoparticle detection, sizing and manipulating nanoscale objects, optical data storage, and maskless direct-write nanopatterning and nanolithography.
Chen et al., “Highly efficient optical coupling and transport phenomena in chains of dielectric microspheres,” Opt. Lett., vol. 31, pp. 389-91 (2006), and Kapitonov et al., “Observation of nanojet-induced modes with small propagation losses in chains of coupled spherical cavities,” Opt. Lett., vol. 32, pp. 409-11 (2007), both incorporated herein by reference, have reported that a chain consisting of microspheres, either with the same dimension or with size dispersion, can achieve low loss optical transport via the mechanism of whispering gallery modes or nanojet-induced modes, thus opening up the window for microsphere-chain based waveguides and resonators as well as laser surgery.
A variety of other micro- and nanostructures, such as the micro-ellipsoid (Liu, “Ultra-elongated photonic nanojets generated by a graded-index microellipsoid,” Prog. Electromagn. Res. Lett., vol. 37, pp. 153-65, 2013), the hemispheric shell (Hengyu et al., “Photonic jet with ultralong working distance by hemispheric shell,” Opt. Express, vol. 23, pp. 6626-33, (2015)), and the cuboid (Minin et al., “Localized photonic jets from flat, three-dimensional dielectric cuboids in the reflection mode,” Opt. Lett, vol. 40, pp. 2329-32, (2015)), have been demonstrated as efficient PNJ generators. The aforesaid references are incorporated herein by reference.
Although microspheres and microcylinders present exceptional characteristics such as PNJ formation, optical transport with low loss, and super-resolution imaging, some of their inherent properties limit their application. For example, the detection of intrinsic nanostructures and artificially introduced nanoparticles deeply embedded within biological cells requires a long PNJ length, whereas a rapidly convergent PNJ generated by the microsphere or microcylinder is followed by a fast divergence. To obtain a much longer PNJ, the graded-index multi-layer microsphere or microellipsoid, the two-layer dielectric microsphere, the liquid-filled hollow microcylinder, the hemispheric shell, and the microaxicon with specific spatial orientation, have been proposed in recent years. However, the engineering difficulty and complexity of fabricating these PNJ generators, as well as the inevitable side lobes, in turn limit their application in the detection of deeply embedded nanostructures within cells. The side lobes are created from the interference of the unscattered incident field that passes around the edge of the generator, the diverging light of the central lobes of the PNJ, and the light that has scattered multiple times within the generator.
Though a considerable number of publications aiming at exploring the mechanisms beneath the unusual imaging properties of microspheres have appeared in recent years, no complete theoretical model has yet been adduced that can fully explain the observed super-resolution capability of microspheres. The observed characteristics of microspheres likely stem from the combined effects of evanescent wave coupling close to the surface of the microsphere and their conversion into propagating waves, the relatively high refractive index of microsphere that induces shrinkage of the illumination wavelength, and the properties of the PNJ.
Yang et al., “Super-resolution imaging of a dielectric microsphere is governed by the waist of its photonic nanojet,” Nano Lett., vol. 16, pp. 4862-70 (2016) (hereinafter, “Yang 2016”) incorporated herein by reference, experimentally validated that shrinking the waist of the PNJ of a dielectric microsphere results in higher lateral resolution, paving a reasonable way to guide the design of super-resolution components. Specifically, the goal is to reduce the full width at half maximum (FWHM) waist of the PNJ. The narrow PNJ is vital to confocal microscopy because the imaging performance of a confocal microscope is closely related to how tightly the illumination light can be focused.
Wu et al., “Modulation of photonic nanojets generated by microspheres decorated with concentric rings,” Opt. Express, vol. 23, pp. 20096-103 (2015), incorporated herein by reference, reported a PNJ with a FWHM waist of 0.485λ (λ=0.4 μm) by engineering a microsphere with four uniformly distributed rings etched at a depth of 1.2 μm and width of 0.25 μm. However, the smallest FWHM PNJ generated by an isolated structure that has been reported, by Wu et al. and others, is larger than λ/3.
Another noteworthy drawback of the microsphere, which is due to its fully curved surface, is the difficulty in handling, moving, and assembling a single microsphere or, more generally, microsphere arrays. Wang et al., “Super-resolution optical microscopy based on scannable cantilever-combined microsphere,” Microsc. Res. Tech., vol. 78, pp. 1128-32 (2015), incorporated herein by reference, proposed a cantilever-combined microsphere to scan over the sample surface to form a full image with post-processing. The method works similarly to a near-field scanning microscope (NFSM) and is thus limited by a low serial scanning speed. Others have proposed to embed microspheres into movable thin-films to precisely align the limited field of view (FOV) within a desired location and to meet the demands of large-area inspection. However, thin-films with refractive index larger than 1 inevitably change the ambient of the microspheres. This necessitates large index microspheres in consideration of the refractive index contrast needed to form the PNJ.
Gu et al., “Subsurface nano-imaging with self-assembled spherical cap optical nanoscopy,” Opt. Express, vol. 24, pp. 4937-48 (2016) (incorporated herein by reference) has proposed a self-assembled spherical cap optical nanoscopy for subsurface nano-imaging, similar to wavelength-scale lens microscopy and shape-controllable microlens arrays developed by others. This design provides a more straightforward way to adjust the effective FOV by moving the substrate and performing image stitching. However, Gu's design, which has only one curved surface, prevents the wavefronts inside the structure from being adequately focused, which may limit the resolution. Gu's structure does not fall within the present definition of an asymmetric structure, as taught and claimed below, because it lacks a waveguide pedestal, which is a critical design element used in the present invention to control the relative phases of the interfering eigenmodes of the waveguide. Moreover, Gu's structure consists of only a single transmissive element.
Recently, low loss and stable optical transport through a chain of microspheres with the same or varied size has been validated and understood as the effect of whispering-gallery modes (WGMs) (as discussed by Chen et al., “Highly efficient optical coupling and transport phenomena in chains of dielectric microspheres,” Opt. Lett., vol. 31, 389-91 (2006)) or periodically focused modes (PFMs) (discussed by Allen et al., “Microsphere-chain waveguides: Focusing and transport properties,” Appl. Phys. Lett., vol. 105, 021112 (2014)), both of which references are incorporated herein by reference. Generally, in a microsphere-chain, however, the radius is the only degree of freedom (DOF) that can be adjusted to control the photons for a given material and excitation.
With the semiconductor industry demanding decreased critical dimension (CD) and increased circuit intricacy, it is becoming more challenging to balance the requirement of accuracy, non-destruction, and high speed aerial inspection in detecting killer defects on patterned wafers. A method of nanoscale defect detection that does not suffer from the aforesaid deficiencies would be, therefore, highly desirable.